It was a close-run thing at a packed-out at the Signal Iduna Park for the German champions, who struggled to find the net despite controlling the game over long periods, with Mats Hummels even missing a second half penalty. Robert Lewandowski saved the day late on, rifling home from the winner from a couple of metres out.
Despite coming undone at this stage of the competition last season - eventually finishing bottom of their group - Dortmund coach Jürgen Klopp showed no sign of timidity and fielded attacking duo Mario Götze and Marco Reus together in his starting line-up for the first time. Yet it was their midfield partner Jakub Blaszczykowski who was liveliest early on, getting past left-back Daley Blind with ease.
Nevertheless, it was the guests who had the first clear-cut chance of the half when ex-Hoffenheim forward Ryan Babel fed Christian Eriksen after Ilkay Gündogan had carelessly given the ball away in midfield. However, Roman Weidenfeller was swiftly off his line to narrow the angle and was able to smother the shot.
No cutting edge
The sight of goal seemed to lift the guests and they were subsequently more confident, even if they did sit deep with the aim of hitting their hosts on the counter. Dortmund continued to get behind the Ajax back line, almost exclusively down the right flank, but a combination of poor deliveries and some excellent last gasp tackling kept the game goalless.
Babel should have given Ajax the lead early in the second period, but he lost his composure and headed over unmarked from close range. Moments later it was Lewandowski's turn to squander a golden opportunity, blazing his shot over the bar from the edge of the area having already done the hard work in getting past two defenders.
Hummels should have put the Yellow-Blacks in front from the penalty spot after Ricardo van Rhijn brought down Götze, but the centre-back's side-footed effort was weak and Kenneth Vermeer saved comfortably. In the closing stages Dortmund increased the pressure once again and restricted their guests to sporadic breaks forward, but even then they struggled to convert their dominance into chances.
Just as it looked as if the points would be shared, Lewandowski controlled Marcel Schmelzer's cross, skipped past his marker and smashed past Vermeer. It was a huge relief for their hosts, especially with tough games against Manchester City and Real Madrid up next.
Dortmund: Weidenfeller - Piszczek, Subotic, Hummels, Schmelzer - Gündogan (Gündogan 89'), Kehl - Blaszczykowski (Perisic 73'), Götze (Schieber 88'), Reus -Lewandowski
Ajax: Vermeer - van Rhijn, Alderweireld, Moisander, Blind - Poulsen - de Jong, Eriksen - Sana, Boerrigter - Babel (Schöne 79')
Goals: 1-0 (Lewandowski 87')